physics, has to do with those phenomena of the atmosphere, the ocean, or the magnetic state of the earth, which are not controllable by man, and which can not, therefore, be repeated at pleasure in the laboratory, but must be observed when and where they occur. The same applies to geology, which is the application of physics, chemistry and even biology, or any science whatever, to the earth, in relation to its physical constitution and its history. Geography deals with the face of the earth, and uses the results of geology to study the earth as fit to be the dwelling place for man. There remain the technical applications of physics in all kinds of engineering, civil, mechanical, electrical, chemical or mining, involving the strength of materials, elasticity and the direction of the natural sources of energy to the purposes of man. All these applications of physics need, and are highly susceptible to, mathematical treatment, and for that reason they are the most perfectly developed of all the sciences.
Let us now turn to the biological sciences. The two fundamental divisions, zoology and botany, dealing with animals and plants, seem to run continuously one into the other, like chemistry and physics. Under both we have the subdivisions of morphology for the study of form and physiology for function. Under zoology we put anatomy, and the various more specialized sciences which find their technical application in medicine. There still remain anthropology, the study of man and his practises, psychology, which deals with the workings of what we call his mind, or that of animals, sociology, properly a part of anthropology, dealing with man when living with his fellows, and economics striving to teach him how to get along with them still better.
This classification is admittedly rough, but it does not separate closely connected things as some that I have seen do. For those who desire finer splitting I refer to the classification of the Scientific Congresses of St. Louis in 1904. Of these biological sciences the methods are somewhat different, they are mostly still in the descriptive stage, and have rarely attained sufficient quantitative information to be capable of mathematical treatment. And yet that must be their ultimate object, for without mathematics there is no exact description. That this is not impossible even in biology may be seen from the following example. If a bacterial culture be inoculated into a jelly with the point of a needle, it will be seen under the microscope to grow in all directions from the original center, and if pains are taken to ensure the physical homogeneity of the jelly the shape of the colony will be an almost perfect circle. If the diameter of this circle be measured at regular intervals, I have no doubt that a quantitative law of growth can be deduced, and even a differential equation found, which will turn out to resemble that of certain physical phenomena, say the conduction of heat. We may observe that the instruments and methods of the physi-
